Given a replicated database, a divergent design tunes the indexes in each replica differently in order to specialize it for a specific subset of the workload. This specialization brings significant performance gains compared to the common practice of having the same indexes in all replicas, but requires the development of new tuning tools for database administrators. In this paper we introduce RITA (Replication-aware Index Tuning Advisor), a novel divergent-tuning advisor that offers several essential features not found in existing tools: it generates robust divergent designs that allow the system to adapt gracefully to replica failures; it computes designs that spread the load evenly among specialized replicas, both during normal operation and when replicas fail; it monitors the workload online in order to detect changes that require a recomputation of the divergent design; and, it offers suggestions to elastically reconfigure the system (by adding/removing replicas or adding/dropping indexes) to respond to workload changes. The key technical innovation behind RITA is showing that the problem of selecting an optimal design can be formulated as a Binary Integer Program (BIP). The BIP has a relatively small number of variables, which makes it feasible to solve it efficiently using any off-the-shelf linear-optimization software. Experimental results demonstrate that RITA computes better divergent designs compared to existing tools, offers more features, and has fast execution times.